# Classification of homogeneous Einstein metrics on pseudo-hyperbolic spaces

Indexed on: 07 Sep '13Published on: 07 Sep '13Published in: Mathematics - Differential Geometry

#### Abstract

We classify the effective and transitive actions of a Lie group G on an n-dimensional non-degenerate hyperboloid (also called real pseudo-hyperbolic space), under the assumption that G is a closed, connected Lie subgroup of an indefinite special orthogonal group. Under the same assumption on G, we also obtain that any G-homogeneous Einstein pseudo-Riemannian metric on a real, complex or quaternionic pseudo-hyperbolic space, or on a para-complex or para-quaternionic projective space is homothetic to either the canonical metric or the Einstein metric of the canonical variation of a Hopf pseudo-Riemannian submersion.